Math Problems Aligned to the Common Core

Illustrative Mathematics is a great resource that brought together teachers, math educators and mathematicians to create mathematical tasks aligned to each standard of the Common Core. There are currently over 1000 tasks, from grades K through 12. Because it is K-12, some tasks will need to be adapted, but because it is K-12, there are rich materials for adult education students at all levels, from ABE to HSE.

There are a few different resources on the site, but I think the one that will be most useful to adult education math teachers are the tasks themselves.

There are a few ways to search for tasks. One nice way to find tasks is to use the search feature, represented by a magnifying glass at the top of the Illustrative Math window. The search box works the same way as putting quotation marks around a term when searching on Google – which is to say, even if you do not put quotation marks, it only shows results that exactly match the keywords you enter. For that reason it is better to be broad in your use of keywords – there are other ways to focus the results.

For example, when I enter “Volume” as a keyword, I get 55 results. If you look to the left of the screen, you will see “Filter Results By”. Click on “Grades” and you will see that the 55 results span from 5th grade to High School. You can then filter the results by choosing specific grade levels. For example, if you choose grades 6, 7 and 8 (a good place to start looking for tasks for HSE students), the number of results goes down to 25. Then you can browse the tasks by clicking on the different titles.

One fun problem I found this way is called Drinking the Lake. It is a task that asks students to calculate the amount of water a person drinks over a lifetime and use that information to consider the size of a container needed to hold that amount of water and finally whether a person could drink all of the water in a lake – Crater Lake in Oregon is the example given, though you could use a local lake just as easily. As with all of the tasks, there are teacher commentary and solution methods (including the answers) underneath. The teacher commentary is generally interesting, explaining things like the purpose of the task, how it fits into the content area, sometimes relevant information (like the dimensions of Crater Lake) and teaching suggestions, sometimes including extension problems. The solution methods are helpful, but they are no means exhaustive.

Another search I did to get started was using the keyword, “Circle”. I filtered the 153 results, again using the 6, 7 and 8th grade tasks and that left 25. Two interesting ones (of many) are Eight Circles and Wedges of a Circle. Wedges of a Circle in particular is interesting because of what it is asking students to do. The situation in the task is that two students have worked on a project to explain why the area of a circle can be found using the formula A = πr2. One of the students is absent and the other student is looking at three pictures from their project and trying to understand them. The task is to help him by writing an explanation of how the provided pictures could be used to derive the formula for the area of a circle. I like the task because it assesses conceptual understanding and asks students to use other content they’ve learned (in this case, how to find the area of a rectangle or a parallelogram) to make connections to newer content. It is a useful way to think about area and it challenges students to express their mathematical thinking in words.

One nice problem I found using ratios and proportional reasoning is called The Price of Bread.  This problem is interesting because it connects to Economics (the idea of inflation, minimum wage, buying power of a $1) and Social Studies (FDR, the New Deal, the Fair Labor Standards Act of 1938). The task asks students to look at some data about the average cost of bread in each decade from 1930-2010 and the Federal Minimum Wage during that same time. Then they have to fill in a few charts, calculating percent increases, making observations and building to the question, “In which decade were people who earn minimum wage most affected by inflation? Explain.” One recommendation I have is to start off by just giving students the last chart without the column about percent cost and without any questions. It doesn’t take long to use the info provided to make your own. It is great to allow students to just talk about what they notice and find out what questions they have. Percentages are a useful tool for making comparisons, but it’s nice to give students time to connect to the real-world ideas and decide for themselves what math to bring in, at least to begin.

One problem I thought was interesting for non-mathematical reasons is called Lincoln’s Math Problem. It is a multi-step simple interest problem. The thing that makes it interesting is that President Lincoln worked on the problem sometime in the 1820s (when he was around 17) – and the task includes photographs of his solution!

Another useful way to search for tasks is by the 8 Mathematical Practice Standards of the Common Core. Phil Daro, one of the writers of the Common Core Math Standards has said the Math Practices are a way to define the content of students’ mathematical character. They are not about how much math content you know, but more about your attitudes and what you do to make sense of and learn math. Illustrative Mathematics offers resources for each of the 8 practices, including tasks and videos. For example, click on the Math Practice #3 “Construct Viable Arguments and Critique the Reasoning of Others” and you’ll find tasks from the lower levels on up, including a good challenging problem from HS, called The Cash Box. One thing I like about that problem is that you can solve it using a system of equations, but I’ve also had students solve it through solid reasoning, using pictures and charts.

In general, Illustrative Mathematics is a good place to find interesting problems to supplement whatever content you are exploring with your students.

I’m really curious about what other tasks people find and use with their students. The ones mentioned above are only a small taste of all that is available. Please add a comment below and let us all know which tasks worked and what level students they worked for.

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About Mark Trushkowsky

Mark enjoys doing math problems that take weeks, family sing-a-longs and reading late into the night. At 16, he believed the next revolution would be waged through poetry. Now he believes it is adult basic education. But he still likes poetry. Mark has worked in adult literacy and HSE since 2001. He is a founding member of the NYC Community of Adult Math Instructors (CAMI). He was born and raised in Brooklyn where he lives happily ever after with his partner Sarah and their daughter Liv. Follow me on Twitter (@mtrushkowsky)

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