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Weekly Math Poll – Systems of Inequality

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Task #1
The context of the problem is a business that makes hats, both by machine and by hand. In the first problem, students need to model an inequality between their budget, $2000, and the cost of making each type of hat. Often students don’t know where to start with word problems, so this task provides some supports in the scratchpad. If you think your students don’t need the extra support, feel free to remove it by clicking on scratchpad settings after you have copied the task into your account.

Student view of task with scratchpad

Task #2
The next problem is another opportunity for them to model an inequality from a word problem. Some students may be able to intuitively see that if over 50% are made by hand then y>x. Others will need some help, so the scratchpad has some steps to get them working. When reviewing the problem with the class, you can always use this pre-saved bookmark called “Great Work!” (Note: you can access bookmarks by clicking on the “Bookmarks” tab when viewing results.)

Task #2 with steps illustrated on the scratchpad

Notice how the scratchpad helped the student get started with writing down what they know, then putting it together to solve the problem. If students write the final answer as y/(y+x)>0.5 (or any variation of it) they will get it right, make sure you go over that this is the same as y>x before the next problem.

Task #3
This is a great example of how you can spice up a multiple choice question. There is a pre-made graph and a blank table on the scratchpad to help them connect different representations of y>x.

Scratchpad with different representations of y>x

Task #4
This problem has the inequality from task 3 on the scratchpad. The major advantage of this is even if your students got it wrong in task 3, they won’t be building off a mistake moving forward. If you are running a teacher led poll, they won’t be able to look ahead. This task is harder than the last one, remember to remind them to use a table or plot some points. If you want, you can always add hints on the scratchpad by going to “Scratchpad Setting” when editing the task.

Scratchpad with inequality from previous task on the scratchpad

The final problem gives them practice with testing points in a system of inequalities while remembering the parameters of the original problem. Students are given a graph of the system of inequalities to help them draw connections between different representations. Remind them as they work that they can draw on the graph (using the scratchpad) to plot points and see which of the shaded regions they are in.

Get started by previewing the poll right now, or login to wootmath.com and search for Systems of Inequality in the Shared Gallery.

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Visit the page on Formative Assessment for more information on implementing these strategies in your classroom.

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Weekly Math Poll – Algebra I Review

Weekly Math Poll – Algebra I Review

This week's math poll asks students to convert between forms of linear equations and explain their preferred strategy for finding a line through two points or a slope and a point.

Task #1

This task has students convert the given equation into standard form. Encourage your students to use the scratchpad to show their thinking!

Task 1 prompt

Task #2

The next task has students convert the given equation into slope intercept form. Encourage them to use the expression editor, which makes it easy to work with and manipulate equations. 

Task 2 prompt

Task #3

In the third task, students are asked to determine which equation they would use to find a line through the points (-5, -4) and (0,8). In this case students can choose from more than one answer – hence it is important to encourage them to show their work and strategy when solving the problem.

Task 3 prompt

Task #4

In the fourth task, students are asked to find a line with a slope of 5 through the point (0,8). Again, multiple answers are possible – so students should explain their work.

We encourage you to modify this task and content to align it with similar content. You can copy the poll and modify or delete any task and also make new ones. Please reach out with any questions or comments, we’re here to support you!

Get started by previewing the poll right now, or login to wootmath.com and search for the Algebra I Review poll in the Shared Gallery.
Preview the Poll
Visit our page on Formative Assessment for more information on implementing these strategies in your classroom. Stay tuned for next week’s poll!

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Weekly Math Poll – New Job

Weekly Math Poll – New Job

This week’s math poll uses the context of a new job and commute costs to learn about systems of equations, functions and linear equations. Students model various situations based on hours worked and price of commute. This poll ends with an opportunity for students to use their computations to make value judgements about if they think the benefits outweigh the costs.

Task #1

New job description

The first task asks students to make a function that models profit per hour, taking into account the $10 of bus fare. In addition to being a relevant context that will help you answer the inevitable question of “When am I ever going to use this in ‘real life’?”, this task highlights two features of Woot Math Polls, equivalence and custom legends of common responses. The short answer task is designed to accept multiple versions of any correct answer. If your students write f(x)=-10+15x they will still get it right; the same goes for y=15x-10 and y+10=15x. We even allow scaled versions of the equation, although it would be unlikely that a student would write 2y=30x-20, though they would still get it right. If you want to change any of the equivalence options, simply open the task and click on the gear icon, the following menu will appear:

Equivalence settings

If you don’t want to accept y in place of f(x) you can deselect it. If you don’t want to accept X in place of x (we recommend not making it case sensitive since some keyboards automatically capitalize) you can select the “Match Case” option. Scaling lets you accept larger and smaller versions of equivalent equations.

The prompt asks for the function to be written as f(x) but we decided to allow y as well for correct answers since if the student is getting this close, they are doing the math right and can get feedback later on which form to put it in. But wouldn’t providing this feedback be tedious and hard to scale to my 30+ students?

I’m glad you asked. That’s where the custom legend comes in. Student responses are automatically categorized based on a custom legend that can be tailored to each problem. This task has the following custom legend:

Custom Legend settings

The custom legend looks from the top down so it is important to have the correct answer first. If they did not account for the return bus fare, their response will show up blue on your dashboard. If you want them to have feedback about f(x) vs y without telling them they are wrong you can see who typed y in their answer (regardless of if they were correct) and remind them to pay attention to the prompt. If you want to praise students for getting close by correctly modeling the rate, you can see those responses in green. By automatically categorizing your responses, this task helps you provide more nuanced feedback and move your students learning forward.

Task #2

The next task has students model the same relationship but as a function of total hours, h instead of hours worked, x. In this case, h=x+2 so replacing x with h-2 will get you the correct answer.

Task #2 statement

But wait! Isn’t f(h)=15h-40 equal to f(h)=15(h-2)-10? Yup! That’s why this task has no assigned correct answer. After students respond you can display the results and have them discuss (in groups if you want) what they all think the correct answer is. Also, if students finish early, you can ask them to find the other correct answer as a challenge. This task also provides an opportunity to review equivalence and distribution.

Task #3

Task #3 Description

In the third task, students model an old job where they made a commission of 20 per sale plus $10 per hour but are maxed out at $100 per day. This task, when combined with the next one gives them more opportunities to work on modeling and also adds some variables that take value judgements and let them connect their own out of class experiences. How hard is it to sell a bike? If you sold a lot, would it be worth it to go home early? How many hours a day do you want to work?

Task #4

Task #4 Description

The final task has them compute the convergence point of the two jobs. This gives them more data to address the question of if they should take the new job or not. There is no correct answer but you can expect student responses to pull in topics ranging from how many hours they want to work, if they like bus rides or not, if they had a car or carpooled if it would be shorter, and if they value having a higher wage more than convenience.

We encourage you to modify this task and content to align it with similar content. You can copy the poll and modify or delete any task and also make new ones. Please reach out with any questions or comments, we’re here to support you!

Get started by previewing the poll right now, or login to wootmath.com and search for the New Job poll in the Shared Gallery.

 
Preview the Poll
Visit our page on Formative Assessment for more information on implementing these strategies in your classroom. Stay tuned for next week’s poll!

Woot Math
All Posts »