This activity is excerpted from Minilessons for Math Practice, Grades 3–5, by Rusty Bresser and Caren Holtzman (Math Solutions Publications, 2006). Amy Jackson presented this lesson to her students in Florence Elementary School in San Diego, California. In this dice activity, the class works together to generate the numbers one through twelve in order. Clear the Board offers opportunities for mental computation and helps build students’ number and operation sense. Students need to think flexibly and consider many possibilities in order to find the solutions to the computation challenges involved.
Amy Jackson wrote the numbers 1 through 12 vertically on the board and asked her students if they’d like to play a game. Their response was positive.
“Great,” she replied. “This game is called Clear the Board. Our goal is to systematically get rid of each number I listed. We have to get rid of the numbers in order, beginning with one first and then moving to two, and all the way to twelve.
“I’m going to roll three dice. I’ll write the numbers rolled on the board so you can see what came up. Then you need to think about how you can use these numbers to make the number one. You may use any operation—addition, subtraction, multiplication, or division—or a combination of operations. When you find a way to make the number one, I’ll cross off the one on the board and we’ll move on to the next number, two. Ready? Here I go.”
Amy rolled a 1, a 3, and a 5 and wrote these numbers on the board.
Amy was surprised that students appeared to be struggling. Why didn’t they just point out that one of the dice came up with a 1? she wondered. Then she realized her directions might not have been clear enough.
“I need to clarify something,” she told the class. “Even though there are three numbers, you don’t need to use all of them. You can use one, two, or all three of the numbers rolled to make the number you need.”
Marcello raised his hand. “How about five minus three minus one?” he suggested.
While Amy was expecting a simpler solution, she wrote Marcello’s idea as an equation on the board next to the 1. Adriana suggested the need for parentheses around 5 – 3. Technically parentheses are not required in this situation; however, their use is not incorrect and adds clarity. Amy decided to include them. She then pointed out that since she had rolled a 1, they could use just that 1, and she recorded that on the board too.
1 (5 – 3) – 1 = 1, 1 = 1
“OK, now that we’ve made one, we can cross it off. We’re on our way to clearing the board. Next up is two.”
“Three take away one is two,” Enrique announced.“You could also do five minus three,” Jamal pointed out.
Amy wrote equations for their ideas next to the 2 and then crossed off the 2. Now that the students understood the mechanics of the activity, she gave them time to talk in groups about ways to make the rest of the numbers. Soon the board filled up with a variety of solutions for the next few numbers. While Amy was impressed with the students’ flexible thinking and comfort with mental computation, she was concerned that the game would go on and on if she didn’t set a limit. The students were more interested in finding multiple solutions for each number than moving on to the next number. To keep the game moving, Amy decided to limit responses to one equation for each number. In a few minutes the board looked like this:
- (5 – 3) – 1 = 1, 1 = 1
- 3 – 1 = 2, 5 – 3 = 2
- 3 = 3, (5 + 1) – 3 = 3, (5 – 3) + 1 = 3
- 3 + 1 = 4, 5 – 1 = 4
- 5 = 5, 5 x 1 =5, 5/1=5
- 5 + 1 = 6
- (5 + 3) – 1 = 7
- 5 + 3 = 8
- 5 + 3 + 1 = 9
- (3 – 1) x 5 = 10
The class got stuck on eleven, so Amy told the students it was time to roll again. Before rolling, she asked a question to assess their comfort with the various operations.
“So,” she said, “I’m going to roll the three dice again. What numbers would you like to get now?”
“A five, a six, and a one,” Cristina offered.
“A five, a six, and anything would work,” Kendrick pointed out. “How about a four, a four, and a three?” suggested Christine. “Or a two, a three, and a six,” J. P. added.
This quick question showed Amy that her students were comfortable breaking eleven apart in different ways but were not as comfortable thinking about operations other than addition. Perhaps with more time and practice, they would open up their thinking.
She rolled the dice and got two 5s and a 1. She wrote these numbers on the board below where she’d written the first roll. Then she turned to the class.
“Tough one, huh?” she teased.
“Just put five plus one plus five,” Kenyatta directed. Amy wrote the equation next to the 11 on the board.
11) 5 + 1 + 5 = 11
“Aren’t you supposed to put parentheses, Ms. Jackson?” Jessie challenged. “No,” J. P. disagreed. “We don’t need them.”
“Let’s check,” Amy suggested. She pointed to the first 5 and the 1. “What’s five plus one?” she asked the class.
“Plus five more equals?” “Eleven.”
“OK,” Amy continued, “let’s see what happens if we start with the other two numbers.” She pointed to the 1 and the second 5. “What’s one plus five?” she asked.
She pointed to the first 5. “Plus five more?” “Eleven.”
“Hmm,” she concluded, “we get the same answer regardless of where we start. So we don’t really need parentheses for this addition equation.” She wrote on the board:
(5 + 1) + 5 = 5 + (1 + 5)
Although this wasn’t the time to go into a lengthy discussion about the purpose of parentheses or the associative property, it was a nice opportunity to model the concept and notation briefly.
Amy gave the students a minute to talk to a partner about how to use these rolls to make twelve. After some computational gymnastics, the students agreed that they couldn’t make twelve with those three numbers, so Amy rolled again. This time she got a 5, a 2, and a 1. She wrote these numbers on the board below the previous roll. The students took a minute to consider the possibilities. Christine raised her hand.
“I’ve got one,” she announced. “Five plus one times two.”
“Do I need to use parentheses for that equation?” Amy asked, reinforcing their prior discussion.
“Yes,” Christine told her. “Put them around the five plus one.”
Amy wrote the equation on the board and had the class double-check to make sure everyone agreed.
(5 + 1) x 2 = 12
Amy crossed out the 12 on the board and congratulated the students for clearing the board. She asked how many rolls it took for them to accomplish their task. Since she had written each roll on the board, the students had an easy reference. Amy wondered aloud if they thought it would take more or less than three rolls when they played next time. Leaving them with something to think about set the stage for future experiences with Clear theBoard.
Cheating on homework is much easier and popular than cheating on in-class assignments. The teacher cannot control the actions of his/her students outside the class. It provides students with the certain benefits. In the age of modern technologies, it is simple to learn how to cheat on homework of any complexity and urgency. No matter what topic a student should cover, the world of internet will offer a quick solution.
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The best way to explain how to cheat on homework is by offering a professional online writing & editing services established by the top UK & US writers who wish to help students with their performance.
How to Cheat on Homework: Reasons to Do That
If you are reading this article, you wonder how to cheat on homework. The reasons may be different:
- A great number of writing assignments
- Difficult tasks
- Lack of time
- Absence of the required sources
Modern students have more tasks than their parents and grandparents used to have ages ago. The research has proved that an hour-1,5 hour is good when it comes to after-class writing. Not many schools & colleges support that idea, and students around the world suffer having an incredible amount of tricky assignments to accomplish in one night: AP essays, book reports, research papers, case studies, math problems, etc.
The primary thing is to explore how to cheat on your homework using old methods.
Traditional, Time-Tested Ways to Trick the Teacher!
To begin with, read about the traditional ways to cheat!
- Make friends with an older guy who is smart and competent to write a short essay twice per week to help a younger friend who would give a cookie to him.
- Paraphrasing. Discover the answer in the shape of long response/essay/research paper on the web and rewrite the full work making it 100% original. Note that it is important to change the structure of the text as replacing the words with synonyms will not make it 100% unique.
- Focus on one brief statement to share in class. Literature class students have to retell the story in front of the class to prove they have read the assigned material. Some volunteers decide to answer before others. Those witty guys who raise their hands initially look super smart to their teachers. While they start answering from the easy part, the teacher loses his interest, thinking a student knows the whole thing and starts ‘attacking’ other slowpokes.
- Download the related film or watch a video online. Even if the video interpretation is a bit different from the book plot, it is better than having no idea of what to say. Some of the history movies are good – why should you waste your time on reading?
- Share the homework with friends: break the long reading material into several blocks and decide which one of you will read particular parts to catch up with the deadline and not get distracted. Help each other in class.
- Get together with the team and brainstorm! It is an excellent practice, which will save a person many times in the future because modern business environment requires brainstorming in many situations.
- Read the summary of the chapter without going into details – focus on keywords.
- Copy the answers from another student. The one has to be lucky to copy the correct answers, make it properly, and stay undetected by the strict teacher.
If it seems complicated, move to the simpler methods available thanks to the rapid technological progress.
How to Cheat on Math Homework?
Services like QuickMath help to answer, “how to cheat on math homework?” They are free of charge, and students may try them. They do not guarantee 100% accurate answers all the time, but it is better than having no response by the due date.
Why Is It Important to Conduct an Internet Research? Being at this website means you know the ways to do a search engine search. Highlight the necessary keywords while reading the problem description, place them on a separate piece of paper, and insert into the Google search field. In case there is a specific question with the answer options “yes”/”no,” enter the double quotes around the search query. Many students face the same math problem every day. This way, a student will find several versions of the answer, and the most common one is a correct solution. Example of how to cheat on my math lab homework using Internet search:
“How long does it take for an automobile driving at a speed of 60.0 miles/hour to pass 200 feet?”
Type the question the way it appears in a prompt. Add some keywords if necessary. An answer to the question of this type will show up in a few seconds at one of the student forums or websites like Quora where users tend to ask each other different questions.
“Copy & paste the problem’s prompt into a Google search field with the double quotes. If you skip that step, the engine will come up with thousands or even millions of possible answers, and part of them will not be correct. Why should a student risk? Besides, without specifying the question with the help f double quotes, a user risks obtaining a plenty of spam websites offering vehicles for sale, rent, related videos, and more garbage.”
Brandon Johnson, a university tutor and online essay/resume writer at JustDoMyHomework.
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How about Cheating on Homework with Special Apps?
Cheating on homework becomes easy when some special mobile applications step in. Do not hope that these smart assistants will complete a statistical report or research paper in history for you. These tools help to make the process faster and simpler by adding fun plus extra options. [Learn here how to do homework fast].
Students who prefer using iPhones will enjoy iHomework. It helps to understand how to cheat on homework by keeping track of the assignments by slicing & dicing in many different ways. The software categorizes the tasks by the exact deadline. It prevents a person from postponing – choose to classify by week, month, or course. Students may link the reading texts to the target tasks. It is the way to avoid digging through a tone of papers to get the required data.
Another opportunity is to tick the locations of different courses. This feature will prevent the student from getting lost in case a college or university has a big campus and overall territory. Thanks to the sync with iCloud, students who use Apple devices may access any learning materials they stored at any time and any moment.
How to cheat on MyMathLab online homework? The software was created to provide an effective homework help for college students who experience problems with high math, algebra, geometry, etc. The best thing about it is the availability of live online tutors 24/7. An app owner has to submit a problem he/she cannot solve alone. Go to the app’s drop-down menu, enter any extra notes, and take a photo of the case study using a device's native camera. Take a clear, high-resolution photo. In something like a couple of fo minutes, the assigned tutor will guide a student through the step-by-step solution and provide valuable tips for the future.
It is an educating service, which makes it possible to take the photos of the assignment prompts and submit to the online tutors. These experts respond in several minutes, giving some hints for the solution. They might explain how to write an essay of a certain type, but only a professional essay writing service can complete the assignment of that type from scratch.
That is how to cheat on your homework when feeling overloaded. The top preferred and most effective homework solution is a professional online homework writing service offered by the qualified UK & US authors, and it remains the best solution for ages!