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Math Workbooks for Grade 3

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Third Grade Math Worksheets

Free grade 3 math worksheets.

Our third grade math worksheets support numeracy development and introduce division, decimals, roman numerals, calendars and concepts in measurement and geometry. Our word problem worksheets review skills in real world scenarios. 

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How to Do Homework: 15 Expert Tips and Tricks

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Coursework/GPA

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Everyone struggles with homework sometimes, but if getting your homework done has become a chronic issue for you, then you may need a little extra help. That’s why we’ve written this article all about how to do homework. Once you’re finished reading it, you’ll know how to do homework (and have tons of new ways to motivate yourself to do homework)!

We’ve broken this article down into a few major sections. You’ll find:

  • A diagnostic test to help you figure out why you’re struggling with homework
  • A discussion of the four major homework problems students face, along with expert tips for addressing them
  • A bonus section with tips for how to do homework fast

By the end of this article, you’ll be prepared to tackle whatever homework assignments your teachers throw at you .

So let’s get started!

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How to Do Homework: Figure Out Your Struggles 

Sometimes it feels like everything is standing between you and getting your homework done. But the truth is, most people only have one or two major roadblocks that are keeping them from getting their homework done well and on time. 

The best way to figure out how to get motivated to do homework starts with pinpointing the issues that are affecting your ability to get your assignments done. That’s why we’ve developed a short quiz to help you identify the areas where you’re struggling. 

Take the quiz below and record your answers on your phone or on a scrap piece of paper. Keep in mind there are no wrong answers! 

1. You’ve just been assigned an essay in your English class that’s due at the end of the week. What’s the first thing you do?

A. Keep it in mind, even though you won’t start it until the day before it’s due  B. Open up your planner. You’ve got to figure out when you’ll write your paper since you have band practice, a speech tournament, and your little sister’s dance recital this week, too.  C. Groan out loud. Another essay? You could barely get yourself to write the last one!  D. Start thinking about your essay topic, which makes you think about your art project that’s due the same day, which reminds you that your favorite artist might have just posted to Instagram...so you better check your feed right now. 

2. Your mom asked you to pick up your room before she gets home from work. You’ve just gotten home from school. You decide you’ll tackle your chores: 

A. Five minutes before your mom walks through the front door. As long as it gets done, who cares when you start?  B. As soon as you get home from your shift at the local grocery store.  C. After you give yourself a 15-minute pep talk about how you need to get to work.  D. You won’t get it done. Between texts from your friends, trying to watch your favorite Netflix show, and playing with your dog, you just lost track of time! 

3. You’ve signed up to wash dogs at the Humane Society to help earn money for your senior class trip. You: 

A. Show up ten minutes late. You put off leaving your house until the last minute, then got stuck in unexpected traffic on the way to the shelter.  B. Have to call and cancel at the last minute. You forgot you’d already agreed to babysit your cousin and bake cupcakes for tomorrow’s bake sale.  C. Actually arrive fifteen minutes early with extra brushes and bandanas you picked up at the store. You’re passionate about animals, so you’re excited to help out! D. Show up on time, but only get three dogs washed. You couldn’t help it: you just kept getting distracted by how cute they were!

4. You have an hour of downtime, so you decide you’re going to watch an episode of The Great British Baking Show. You: 

A. Scroll through your social media feeds for twenty minutes before hitting play, which means you’re not able to finish the whole episode. Ugh! You really wanted to see who was sent home!  B. Watch fifteen minutes until you remember you’re supposed to pick up your sister from band practice before heading to your part-time job. No GBBO for you!  C. You finish one episode, then decide to watch another even though you’ve got SAT studying to do. It’s just more fun to watch people make scones.  D. Start the episode, but only catch bits and pieces of it because you’re reading Twitter, cleaning out your backpack, and eating a snack at the same time.

5. Your teacher asks you to stay after class because you’ve missed turning in two homework assignments in a row. When she asks you what’s wrong, you say: 

A. You planned to do your assignments during lunch, but you ran out of time. You decided it would be better to turn in nothing at all than submit unfinished work.  B. You really wanted to get the assignments done, but between your extracurriculars, family commitments, and your part-time job, your homework fell through the cracks.  C. You have a hard time psyching yourself to tackle the assignments. You just can’t seem to find the motivation to work on them once you get home.  D. You tried to do them, but you had a hard time focusing. By the time you realized you hadn’t gotten anything done, it was already time to turn them in. 

Like we said earlier, there are no right or wrong answers to this quiz (though your results will be better if you answered as honestly as possible). Here’s how your answers break down: 

  • If your answers were mostly As, then your biggest struggle with doing homework is procrastination. 
  • If your answers were mostly Bs, then your biggest struggle with doing homework is time management. 
  • If your answers were mostly Cs, then your biggest struggle with doing homework is motivation. 
  • If your answers were mostly Ds, then your biggest struggle with doing homework is getting distracted. 

Now that you’ve identified why you’re having a hard time getting your homework done, we can help you figure out how to fix it! Scroll down to find your core problem area to learn more about how you can start to address it. 

And one more thing: you’re really struggling with homework, it’s a good idea to read through every section below. You may find some additional tips that will help make homework less intimidating. 

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How to Do Homework When You’re a Procrastinator  

Merriam Webster defines “procrastinate” as “to put off intentionally and habitually.” In other words, procrastination is when you choose to do something at the last minute on a regular basis. If you’ve ever found yourself pulling an all-nighter, trying to finish an assignment between periods, or sprinting to turn in a paper minutes before a deadline, you’ve experienced the effects of procrastination. 

If you’re a chronic procrastinator, you’re in good company. In fact, one study found that 70% to 95% of undergraduate students procrastinate when it comes to doing their homework. Unfortunately, procrastination can negatively impact your grades. Researchers have found that procrastination can lower your grade on an assignment by as much as five points ...which might not sound serious until you realize that can mean the difference between a B- and a C+. 

Procrastination can also negatively affect your health by increasing your stress levels , which can lead to other health conditions like insomnia, a weakened immune system, and even heart conditions. Getting a handle on procrastination can not only improve your grades, it can make you feel better, too! 

The big thing to understand about procrastination is that it’s not the result of laziness. Laziness is defined as being “disinclined to activity or exertion.” In other words, being lazy is all about doing nothing. But a s this Psychology Today article explains , procrastinators don’t put things off because they don’t want to work. Instead, procrastinators tend to postpone tasks they don’t want to do in favor of tasks that they perceive as either more important or more fun. Put another way, procrastinators want to do things...as long as it’s not their homework! 

3 Tips f or Conquering Procrastination 

Because putting off doing homework is a common problem, there are lots of good tactics for addressing procrastination. Keep reading for our three expert tips that will get your homework habits back on track in no time. 

#1: Create a Reward System

Like we mentioned earlier, procrastination happens when you prioritize other activities over getting your homework done. Many times, this happens because homework...well, just isn’t enjoyable. But you can add some fun back into the process by rewarding yourself for getting your work done. 

Here’s what we mean: let’s say you decide that every time you get your homework done before the day it’s due, you’ll give yourself a point. For every five points you earn, you’ll treat yourself to your favorite dessert: a chocolate cupcake! Now you have an extra (delicious!) incentive to motivate you to leave procrastination in the dust. 

If you’re not into cupcakes, don’t worry. Your reward can be anything that motivates you . Maybe it’s hanging out with your best friend or an extra ten minutes of video game time. As long as you’re choosing something that makes homework worth doing, you’ll be successful. 

#2: Have a Homework Accountability Partner 

If you’re having trouble getting yourself to start your homework ahead of time, it may be a good idea to call in reinforcements . Find a friend or classmate you can trust and explain to them that you’re trying to change your homework habits. Ask them if they’d be willing to text you to make sure you’re doing your homework and check in with you once a week to see if you’re meeting your anti-procrastination goals. 

Sharing your goals can make them feel more real, and an accountability partner can help hold you responsible for your decisions. For example, let’s say you’re tempted to put off your science lab write-up until the morning before it’s due. But you know that your accountability partner is going to text you about it tomorrow...and you don’t want to fess up that you haven’t started your assignment. A homework accountability partner can give you the extra support and incentive you need to keep your homework habits on track. 

#3: Create Your Own Due Dates 

If you’re a life-long procrastinator, you might find that changing the habit is harder than you expected. In that case, you might try using procrastination to your advantage! If you just can’t seem to stop doing your work at the last minute, try setting your own due dates for assignments that range from a day to a week before the assignment is actually due. 

Here’s what we mean. Let’s say you have a math worksheet that’s been assigned on Tuesday and is due on Friday. In your planner, you can write down the due date as Thursday instead. You may still put off your homework assignment until the last minute...but in this case, the “last minute” is a day before the assignment’s real due date . This little hack can trick your procrastination-addicted brain into planning ahead! 

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If you feel like Kevin Hart in this meme, then our tips for doing homework when you're busy are for you. 

How to Do Homework When You’re too Busy

If you’re aiming to go to a top-tier college , you’re going to have a full plate. Because college admissions is getting more competitive, it’s important that you’re maintaining your grades , studying hard for your standardized tests , and participating in extracurriculars so your application stands out. A packed schedule can get even more hectic once you add family obligations or a part-time job to the mix. 

If you feel like you’re being pulled in a million directions at once, you’re not alone. Recent research has found that stress—and more severe stress-related conditions like anxiety and depression— are a major problem for high school students . In fact, one study from the American Psychological Association found that during the school year, students’ stress levels are higher than those of the adults around them. 

For students, homework is a major contributor to their overall stress levels . Many high schoolers have multiple hours of homework every night , and figuring out how to fit it into an already-packed schedule can seem impossible. 

3 Tips for Fitting Homework Into Your Busy Schedule

While it might feel like you have literally no time left in your schedule, there are still ways to make sure you’re able to get your homework done and meet your other commitments. Here are our expert homework tips for even the busiest of students. 

#1: Make a Prioritized To-Do List 

You probably already have a to-do list to keep yourself on track. The next step is to prioritize the items on your to-do list so you can see what items need your attention right away. 

Here’s how it works: at the beginning of each day, sit down and make a list of all the items you need to get done before you go to bed. This includes your homework, but it should also take into account any practices, chores, events, or job shifts you may have. Once you get everything listed out, it’s time to prioritize them using the labels A, B, and C. Here’s what those labels mean:

  • A Tasks : tasks that have to get done—like showing up at work or turning in an assignment—get an A. 
  • B Tasks : these are tasks that you would like to get done by the end of the day but aren’t as time sensitive. For example, studying for a test you have next week could be a B-level task. It’s still important, but it doesn’t have to be done right away.
  • C Tasks: these are tasks that aren’t very important and/or have no real consequences if you don’t get them done immediately. For instance, if you’re hoping to clean out your closet but it’s not an assigned chore from your parents, you could label that to-do item with a C.

Prioritizing your to-do list helps you visualize which items need your immediate attention, and which items you can leave for later. A prioritized to-do list ensures that you’re spending your time efficiently and effectively, which helps you make room in your schedule for homework. So even though you might really want to start making decorations for Homecoming (a B task), you’ll know that finishing your reading log (an A task) is more important. 

#2: Use a Planner With Time Labels

Your planner is probably packed with notes, events, and assignments already. (And if you’re not using a planner, it’s time to start!) But planners can do more for you than just remind you when an assignment is due. If you’re using a planner with time labels, it can help you visualize how you need to spend your day.

A planner with time labels breaks your day down into chunks, and you assign tasks to each chunk of time. For example, you can make a note of your class schedule with assignments, block out time to study, and make sure you know when you need to be at practice. Once you know which tasks take priority, you can add them to any empty spaces in your day. 

Planning out how you spend your time not only helps you use it wisely, it can help you feel less overwhelmed, too . We’re big fans of planners that include a task list ( like this one ) or have room for notes ( like this one ). 

#3: Set Reminders on Your Phone 

If you need a little extra nudge to make sure you’re getting your homework done on time, it’s a good idea to set some reminders on your phone. You don’t need a fancy app, either. You can use your alarm app to have it go off at specific times throughout the day to remind you to do your homework. This works especially well if you have a set homework time scheduled. So if you’ve decided you’re doing homework at 6:00 pm, you can set an alarm to remind you to bust out your books and get to work. 

If you use your phone as your planner, you may have the option to add alerts, emails, or notifications to scheduled events . Many calendar apps, including the one that comes with your phone, have built-in reminders that you can customize to meet your needs. So if you block off time to do your homework from 4:30 to 6:00 pm, you can set a reminder that will pop up on your phone when it’s time to get started. 

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This dog isn't judging your lack of motivation...but your teacher might. Keep reading for tips to help you motivate yourself to do your homework.

How to Do Homework When You’re Unmotivated 

At first glance, it may seem like procrastination and being unmotivated are the same thing. After all, both of these issues usually result in you putting off your homework until the very last minute. 

But there’s one key difference: many procrastinators are working, they’re just prioritizing work differently. They know they’re going to start their homework...they’re just going to do it later. 

Conversely, people who are unmotivated to do homework just can’t find the willpower to tackle their assignments. Procrastinators know they’ll at least attempt the homework at the last minute, whereas people who are unmotivated struggle with convincing themselves to do it at a ll. For procrastinators, the stress comes from the inevitable time crunch. For unmotivated people, the stress comes from trying to convince themselves to do something they don’t want to do in the first place. 

Here are some common reasons students are unmotivated in doing homework : 

  • Assignments are too easy, too hard, or seemingly pointless 
  • Students aren’t interested in (or passionate about) the subject matter
  • Students are intimidated by the work and/or feels like they don’t understand the assignment 
  • Homework isn’t fun, and students would rather spend their time on things that they enjoy 

To sum it up: people who lack motivation to do their homework are more likely to not do it at all, or to spend more time worrying about doing their homework than...well, actually doing it.

3 Tips for How to Get Motivated to Do Homework

The key to getting homework done when you’re unmotivated is to figure out what does motivate you, then apply those things to homework. It sounds tricky...but it’s pretty simple once you get the hang of it! Here are our three expert tips for motivating yourself to do your homework. 

#1: Use Incremental Incentives

When you’re not motivated, it’s important to give yourself small rewards to stay focused on finishing the task at hand. The trick is to keep the incentives small and to reward yourself often. For example, maybe you’re reading a good book in your free time. For every ten minutes you spend on your homework, you get to read five pages of your book. Like we mentioned earlier, make sure you’re choosing a reward that works for you! 

So why does this technique work? Using small rewards more often allows you to experience small wins for getting your work done. Every time you make it to one of your tiny reward points, you get to celebrate your success, which gives your brain a boost of dopamine . Dopamine helps you stay motivated and also creates a feeling of satisfaction when you complete your homework !  

#2: Form a Homework Group 

If you’re having trouble motivating yourself, it’s okay to turn to others for support. Creating a homework group can help with this. Bring together a group of your friends or classmates, and pick one time a week where you meet and work on homework together. You don’t have to be in the same class, or even taking the same subjects— the goal is to encourage one another to start (and finish!) your assignments. 

Another added benefit of a homework group is that you can help one another if you’re struggling to understand the material covered in your classes. This is especially helpful if your lack of motivation comes from being intimidated by your assignments. Asking your friends for help may feel less scary than talking to your teacher...and once you get a handle on the material, your homework may become less frightening, too. 

#3: Change Up Your Environment 

If you find that you’re totally unmotivated, it may help if you find a new place to do your homework. For example, if you’ve been struggling to get your homework done at home, try spending an extra hour in the library after school instead. The change of scenery can limit your distractions and give you the energy you need to get your work done. 

If you’re stuck doing homework at home, you can still use this tip. For instance, maybe you’ve always done your homework sitting on your bed. Try relocating somewhere else, like your kitchen table, for a few weeks. You may find that setting up a new “homework spot” in your house gives you a motivational lift and helps you get your work done. 

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Social media can be a huge problem when it comes to doing homework. We have advice for helping you unplug and regain focus.

How to Do Homework When You’re Easily Distracted

We live in an always-on world, and there are tons of things clamoring for our attention. From friends and family to pop culture and social media, it seems like there’s always something (or someone!) distracting us from the things we need to do.

The 24/7 world we live in has affected our ability to focus on tasks for prolonged periods of time. Research has shown that over the past decade, an average person’s attention span has gone from 12 seconds to eight seconds . And when we do lose focus, i t takes people a long time to get back on task . One study found that it can take as long as 23 minutes to get back to work once we’ve been distracte d. No wonder it can take hours to get your homework done! 

3 Tips to Improve Your Focus

If you have a hard time focusing when you’re doing your homework, it’s a good idea to try and eliminate as many distractions as possible. Here are three expert tips for blocking out the noise so you can focus on getting your homework done. 

#1: Create a Distraction-Free Environment

Pick a place where you’ll do your homework every day, and make it as distraction-free as possible. Try to find a location where there won’t be tons of noise, and limit your access to screens while you’re doing your homework. Put together a focus-oriented playlist (or choose one on your favorite streaming service), and put your headphones on while you work. 

You may find that other people, like your friends and family, are your biggest distraction. If that’s the case, try setting up some homework boundaries. Let them know when you’ll be working on homework every day, and ask them if they’ll help you keep a quiet environment. They’ll be happy to lend a hand! 

#2: Limit Your Access to Technology 

We know, we know...this tip isn’t fun, but it does work. For homework that doesn’t require a computer, like handouts or worksheets, it’s best to put all your technology away . Turn off your television, put your phone and laptop in your backpack, and silence notifications on any wearable tech you may be sporting. If you listen to music while you work, that’s fine...but make sure you have a playlist set up so you’re not shuffling through songs once you get started on your homework. 

If your homework requires your laptop or tablet, it can be harder to limit your access to distractions. But it’s not impossible! T here are apps you can download that will block certain websites while you’re working so that you’re not tempted to scroll through Twitter or check your Facebook feed. Silence notifications and text messages on your computer, and don’t open your email account unless you absolutely have to. And if you don’t need access to the internet to complete your assignments, turn off your WiFi. Cutting out the online chatter is a great way to make sure you’re getting your homework done. 

#3: Set a Timer (the Pomodoro Technique)

Have you ever heard of the Pomodoro technique ? It’s a productivity hack that uses a timer to help you focus!

Here’s how it works: first, set a timer for 25 minutes. This is going to be your work time. During this 25 minutes, all you can do is work on whatever homework assignment you have in front of you. No email, no text messaging, no phone calls—just homework. When that timer goes off, you get to take a 5 minute break. Every time you go through one of these cycles, it’s called a “pomodoro.” For every four pomodoros you complete, you can take a longer break of 15 to 30 minutes.

The pomodoro technique works through a combination of boundary setting and rewards. First, it gives you a finite amount of time to focus, so you know that you only have to work really hard for 25 minutes. Once you’ve done that, you’re rewarded with a short break where you can do whatever you want. Additionally, tracking how many pomodoros you complete can help you see how long you’re really working on your homework. (Once you start using our focus tips, you may find it doesn’t take as long as you thought!)

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Two Bonus Tips for How to Do Homework Fast

Even if you’re doing everything right, there will be times when you just need to get your homework done as fast as possible. (Why do teachers always have projects due in the same week? The world may never know.)

The problem with speeding through homework is that it’s easy to make mistakes. While turning in an assignment is always better than not submitting anything at all, you want to make sure that you’re not compromising quality for speed. Simply put, the goal is to get your homework done quickly and still make a good grade on the assignment! 

Here are our two bonus tips for getting a decent grade on your homework assignments , even when you’re in a time crunch. 

#1: Do the Easy Parts First 

This is especially true if you’re working on a handout with multiple questions. Before you start working on the assignment, read through all the questions and problems. As you do, make a mark beside the questions you think are “easy” to answer . 

Once you’ve finished going through the whole assignment, you can answer these questions first. Getting the easy questions out of the way as quickly as possible lets you spend more time on the trickier portions of your homework, which will maximize your assignment grade. 

(Quick note: this is also a good strategy to use on timed assignments and tests, like the SAT and the ACT !) 

#2: Pay Attention in Class 

Homework gets a lot easier when you’re actively learning the material. Teachers aren’t giving you homework because they’re mean or trying to ruin your weekend... it’s because they want you to really understand the course material. Homework is designed to reinforce what you’re already learning in class so you’ll be ready to tackle harder concepts later.

When you pay attention in class, ask questions, and take good notes, you’re absorbing the information you’ll need to succeed on your homework assignments. (You’re stuck in class anyway, so you might as well make the most of it!) Not only will paying attention in class make your homework less confusing, it will also help it go much faster, too.

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What’s Next?

If you’re looking to improve your productivity beyond homework, a good place to begin is with time management. After all, we only have so much time in a day...so it’s important to get the most out of it! To get you started, check out this list of the 12 best time management techniques that you can start using today.

You may have read this article because homework struggles have been affecting your GPA. Now that you’re on the path to homework success, it’s time to start being proactive about raising your grades. This article teaches you everything you need to know about raising your GPA so you can

Now you know how to get motivated to do homework...but what about your study habits? Studying is just as critical to getting good grades, and ultimately getting into a good college . We can teach you how to study bette r in high school. (We’ve also got tons of resources to help you study for your ACT and SAT exams , too!)

These recommendations are based solely on our knowledge and experience. If you purchase an item through one of our links, PrepScholar may receive a commission.

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Ashley SufflĂŠ Robinson has a Ph.D. in 19th Century English Literature. As a content writer for PrepScholar, Ashley is passionate about giving college-bound students the in-depth information they need to get into the school of their dreams.

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Signals and systems, 6.003 homework 3 solutions.

This file contains information regarding solutions of homework 3.

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homework 3

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CSE 163, Winter 2020: Homework 3: Data Analysis

This assignment and its reflection are due by Thursday, January 30 at 11:59 pm .

You should submit your finished hw3.py , and hw3-written.txt on Ed and the reflection on Google Forms

You may submit your assignment as many times as you want before the late cutoff (remember submitting after the due date will cost late days). Recall on Ed, you submit by pressing the "Mark" button. You are welcome to develop the assignment on Ed or develop locally and then upload to Ed before marking.

In this assignment, you will apply what you've learned so far in a more extensive "real-world" dataset using more powerful features of the Pandas library. As in HW2, this dataset is provided in CSV format. We have cleaned up the data some, but you will need to handle more edge cases common to real-world datasets, including null cells to represent unknown information.

Note that there is no graded testing portion of this assignment. We still recommend writing tests to verify the correctness of the methods that you write in Part 0, but it will be difficult to write tests for Part 1 and 2. We've provided tips in those sections to help you gain confidence about the correctness of your solutions without writing formal test functions!

This assignment is supposed to introduce you to various parts of the data science process involving being able to answer questions about your data, how to visualize your data, and how to use your data to make predictions for new data. To help prepare for your final project, this assignment has been designed to be wide in scope so you can get practice with many different aspects of data analysis. While this assignment might look large because there are many parts, each individual part is relatively small.

Learning Objectives

After this homework, students will be able to:

  • Work with basic Python data structures.
  • Handle edge cases appropriately, including addressing missing values/data.
  • Practice user-friendly error-handling.
  • Read plotting library documentation and use example plotting code to figure out how to create more complex Seaborn plots.
  • Train a machine learning model and use it to make a prediction about the future using the scikit-learn library.

Expectations

Here are some baseline expectations we expect you to meet:

Follow the course collaboration policies

If you are developing on Ed, all the files are there. If you are developing locally, you should download the starter code hw3.zip and open it as the project in Visual Studio Code. The files included are:

  • hw3-nces-ed-attainment.csv : A CSV file that contains data from the National Center for Education Statistics. This is described in more detail below.
  • hw3.py : The file for you to put solutions to Part 0, Part 1, and Part 2. You are required to add a main method that parses the provided dataset and calls all of the functions you are to write for this homework.
  • hw3-written.txt : The file for you to put your answers to the questions in Part 3.
  • cse163_utils.py : Provides utility functions for this assignment. You probably don't need to use anything inside this file except importing it if you have a Mac (see comment in hw3.py )

The dataset you will be processing comes from the National Center for Education Statistics. You can find the original dataset here . We have cleaned it a bit to make it easier to process in the context of this assignment. You must use our provided CSV file in this assignment.

The original dataset is titled: Percentage of persons 25 to 29 years old with selected levels of educational attainment, by race/ethnicity and sex: Selected years, 1920 through 2018 . The cleaned version you will be working with has columns for Year, Sex, Educational Attainment, and race/ethnicity categories considered in the dataset. Note that not all columns will have data starting at 1920.

Our provided hw3-nces-ed-attainment.csv looks like: (⋮ represents omitted rows):

Year Sex Min degree Total White Black Hispanic Asian Pacific Islander American Indian/Alaska Native Two or more races
1920 A high school --- 22.0 6.3 --- --- --- --- ---
1940 A high school 38.1 41.2 12.3 --- --- --- --- ---
2018 F master's 10.7 12.6 6.2 3.8 29.9 --- --- ---

Column Descriptions

  • Year: The year this row represents. Note there may be more than one row for the same year to show the percent breakdowns by sex.
  • Sex: The sex of the students this row pertains to, one of "F" for female, "M" for male, or "A" for all students.
  • Min degree: The degree this row pertains to. One of "high school", "associate's", "bachelor's", or "master's".
  • Total: The total percent of students of the specified gender to reach at least the minimum level of educational attainment in this year.
  • White / Black / Hispanic / Asian / Pacific Islander / American Indian or Alaska Native / Two or more races: The percent of students of this race and the specified gender to reach at least the minimum level of educational attainment in this year.

Interactive Development

When using data science libraries like pandas , seaborn , or scikit-learn it's extremely helpful to actually interact with the tools your using so you can have a better idea about the shape of your data. The preferred practice by people in industry is to use a Jupyter Notebook, like we have been in lecture, to play around with the dataset to help figure out how to answer the questions you want to answer. This is incredibly helpful when you're first learning a tool as you can actually experiment and get real-time feedback if the code you wrote does what you want.

We recommend that you try figuring out how to solve these problems in a Jupyter Notebook so you can actually interact with the data. We have made a playground Jupyter Notebook for you to use that already has the data loaded. Remember, that playground notebooks on Colaboratory are temporary unless you save them to your Google Drive! If you want to save your work on the notebook, you should make sure you explicitly press the save button and follow the instructions to copy!

Table of Contents

Part 0: Statistical Functions with Pandas

Part 1: Plotting with Seaborn

Part 2: Machine learning with scikit-learn

Part 3: Written Responses

Part 4a: Submit Assignment and Part 4b: Complete Reflection . On Ed, you should submit:

  • hw3-written.txt

Your submission will be evaluated on the following dimensions:

  • Your solution correctly implements the described behaviors. You will have access to some tests when you turn in your assignment, but we will withhold other tests to test your solution when grading. All behavior we test is completely described by the problem specification or shown in an example.
  • No method should modify its input parameters.
  • Your main method in hw3.py must call every one of the methods you implemented in this assignment. There are no requirements on the format of the output, besides that it should save the files for Part 1 with the proper names specified in Part 1.
  • We can run your hw3.py without it crashing or causing any errors.
  • All code files submitted pass flake8
  • Your program should be written with good programming style. This means you should use the proper naming convention for methods and variables ( snake_case ), your code should not be overly redundant and should avoid unnecessary computations.
  • Every function written is commented using a doc-string format that describes its behavior, parameters, returns, and highlights any special cases.
  • There is a comment at the top of each code file you write with your name, section, and a brief description of what that program does.
  • Any expectations on this page or the sub-pages for the assignment are met as well as all requirements for each of the problems are met.

Make sure you carefully read the bullets above as they may or may not change from assignment to assignment!

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Homework 3: Tree Recursion, Sequences, Python Lists, Trees hw03.zip

Due by 11:59pm on Wednesday, July 10

Instructions

Download hw03.zip . Inside the archive, you will find a file called hw03.py , along with a copy of the ok autograder.

Submission: When you are done, submit the assignment by uploading all code files you've edited to Gradescope. You may submit more than once before the deadline; only the final submission will be scored. Check that you have successfully submitted your code on Gradescope. See Lab 0 for more instructions on submitting assignments.

Readings: You might find the following references useful:

  • Section 1.7
  • Section 2.2
  • Section 2.3
  • Section 2.4

Required Questions

Getting started videos.

These videos may provide some helpful direction for tackling the coding problems on this assignment.

To see these videos, you should be logged into your berkeley.edu email.

YouTube link

Tree Recursion

Q1: pascal's triangle.

Pascal's triangle gives the coefficients of a binomial expansion; if you expand the expression (a + b) ** n , all coefficients will be found on the n th row of the triangle, and the coefficient of the i th term will be at the i th column.

Here's a part of the Pascal's trangle:

Every number in Pascal's triangle is defined as the sum of the item above it and the item above and to the left of it. Rows and columns are zero-indexed; that is, the first row is row 0 instead of 1 and the first column is column 0 instead of column 1. For example, the item at row 2, column 1 in Pascal's triangle is 2.

Now, define the procedure pascal(row, column) which takes a row and a column, and finds the value of the item at that position in Pascal's triangle. Note that Pascal's triangle is only defined at certain areas; use 0 if the item does not exist. For the purposes of this question, you may also assume that row >= 0 and column >= 0 .

Hint : Pascal's Triangle can be visualized as a grid rather than a geometric, three-sided triangle. With this in mind, how does the position of the value you are trying to find relate to the positions of the two numbers that add up to it? At what coordinates of the "grid" do we find out the value and don't need further calculations? Remember that the positions are 0-indexed!

Here is a visualization of the grid:

Pascal Grid

Use Ok to test your code:

Sequences and Mutability

Q2: insert items.

Write a function which takes in a list s , a value before , and a value after . It inserts after just after each value equal to before in s . It returns s .

Important: No new lists should be created or returned.

Note: If the values passed into before and after are equal, make sure you're not creating an infinitely long list while iterating through it. If you find that your code is taking more than a few seconds to run, the function may be in an infinite loop of inserting new values.

Data Abstraction

Acknowledgements

This problem is based on one from Structure and Interpretation of Computer Programs Section 2.2.2 .

Mobile example

We are making a planetarium mobile. A mobile is a type of hanging sculpture. A binary mobile consists of two arms. Each arm is a rod of a certain length, from which hangs either a planet or another mobile. For example, the below diagram shows the left and right arms of Mobile A, and what hangs at the ends of each of those arms.

Labeled Mobile example

We will represent a binary mobile using the data abstractions below.

  • A mobile must have both a left arm and a right arm .
  • An arm has a positive length and must have something hanging at the end, either a mobile or planet .
  • A planet has a positive mass, and nothing hanging from it.

Below are the various constructors and selectors for the mobile and arm data abstraction. They have already been implemented for you, though the code is not shown here. As with any data abstraction, you should focus on what the function does rather than its specific implementation. You are free to use any of their constructor and selector functions in the Mobiles coding exercises.

Mobile Data Abstraction ( for your reference, no need to do anything here ):

Implement the planet data abstraction by completing the planet constructor and the mass selector. A planet should be represented using a two-element list where the first element is the string 'planet' and the second element is the planet's mass. The mass function should return the mass of the planet object that is passed as a parameter.

The total_mass function demonstrates the use of the mobile, arm, and planet abstractions. It has been implemented for you. You may use the total_mass function in the following questions.

Run the ok tests for total_mass to make sure that your planet and mass functions are implemented correctly.

Q4: Balanced

Implement the balanced function, which returns whether m is a balanced mobile. A mobile is balanced if both of the following conditions are met:

  • The torque applied by its left arm is equal to the torque applied by its right arm. The torque of the left arm is the length of the left rod multiplied by the total mass hanging from that rod. Likewise for the right. For example, if the left arm has a length of 5 , and there is a mobile hanging at the end of the left arm of total mass 10 , the torque on the left side of our mobile is 50 .
  • Each of the mobiles hanging at the end of its arms is itself balanced .

Planets themselves are balanced, as there is nothing hanging off of them.

Reminder: You may use the total_mass function above. Don't violate abstraction barriers. Instead, use the selector functions that have been defined.

Q5: Finding Berries!

The squirrels on campus need your help! There are a lot of trees on campus and the squirrels would like to know which ones contain berries. Define the function berry_finder , which takes in a tree and returns True if the tree contains a node with the value 'berry' and False otherwise.

Hint : To iterate through each of the branches of a particular tree, you can consider using a for loop to get each branch.

Q6: Maximum Path Sum

Write a function that takes in a tree and returns the maximum sum of the values along any root-to-leaf path in the tree. A root-to-leaf path is a sequence of nodes starting at the root and proceeding to some leaf of the tree. You can assume the tree will have positive numbers for its labels.

Check Your Score Locally

You can locally check your score on each question of this assignment by running

This does NOT submit the assignment! When you are satisfied with your score, submit the assignment to Gradescope to receive credit for it.

Submit Assignment

Submit this assignment by uploading any files you've edited to the appropriate Gradescope assignment. Lab 00 has detailed instructions.

Exam Practice

Homework assignments will also contain prior exam-level questions for you to take a look at. These questions have no submission component; feel free to attempt them if you'd like a challenge!

  • Fall 2017 MT1 Q4a: Digital
  • Summer 2018 MT1 Q5a: Won't You Be My Neighbor?
  • Fall 2019 Final Q6b: Palindromes

Just For Fun Questions

The questions below are out of scope for 61A. You can try them if you want an extra challenge, but they're just puzzles that are not required for the course. Almost all students will skip them, and that's fine. We will not be prioritizing support for these questions on Ed or during Office Hours.

Q7: Towers of Hanoi

This problem was covered in lecture, but feel free to use this question to test your understanding and re-implement the problem. -->

Towers of Hanoi

  • Only one disk may be moved at a time.
  • Each move consists of taking the top (smallest) disk from one of the rods and sliding it onto another rod, on top of the other disks that may already be present on that rod.
  • No disk may be placed on top of a smaller disk.
Hint: Draw out a few games with various n on a piece of paper and try to find a pattern of disk movements that applies to any n . In your solution, take the recursive leap of faith whenever you need to move any amount of disks less than n from one rod to another. If you need more help, see the following hints.

See the following animation of the Towers of Hanoi, found on Wikimedia by user Trixx .

The strategy used in Towers of Hanoi is to move all but the bottom disc to the second peg, then moving the bottom disc to the third peg, then moving all but the second disc from the second to the third peg.

One thing you don't need to worry about is collecting all the steps. print effectively "collects" all the results in the terminal as long as you make sure that the moves are printed in order.

Q8: Anonymous Factorial

This question demonstrates that it's possible to write recursive functions without assigning them a name in the global frame.

The recursive factorial function can be written as a single expression by using a conditional expression .

However, this implementation relies on the fact (no pun intended) that fact has a name, to which we refer in the body of fact . To write a recursive function, we have always given it a name using a def or assignment statement so that we can refer to the function within its own body. In this question, your job is to define fact recursively without giving it a name!

Write an expression that computes n factorial using only call expressions, conditional expressions, and lambda expressions (no assignment or def statements).

Note: You are not allowed to use make_anonymous_factorial in your return expression.

The sub and mul functions from the operator module are the only built-in functions required to solve this problem.

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  19. Homework 3: Data Analysis

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