What The Heck is Illustrative Mathematics?

If you’re not on social media, you may have missed the announcement from the Bensalem School District about their “Math Night” being held at Snyder Middle School on Oct. 19th from 6 pm to 8 pm. The event aims to introduce parents to Illustrative Mathematics, the new math curriculum the Bensalem School District has adopted. This leads to the question, what the heck is Illustrative Mathematics? Didn’t we just get new math a couple of years ago?

A quick Google search only brings up a few sentences from McGraw-Hill which reads

Illustrative Mathematics is a problem-based core curriculum for 21st century learners designed to address content and practice standards to foster learning for all, preparing students to solve problems, reason, communicate, and think critically in the classroom and beyond.

Dig a little deeper and you get this from the developers themselves, Illustrative Mathematics.

IM K–12 Math is a problem-based core curriculum built on the principle that all students are capable learners of grade-level mathematics. Students learn math by doing math. They are encouraged to use their current understanding of math, their lived experiences, and the world around them as resources for problem solving. By starting with what students already know, teachers invite all students to contribute to mathematical learning, centering student thinking, and being responsive as students develop conceptual understanding.

While not the clean-cut explanation one would hope for, what we can pull from both quotes is that Common Core is still the new math and is not going anywhere. But in fact, educators needed help in explaining the Common Core concepts.

Illustrative Mathematics will be the curriculum used to teach Common Core but using real-world problems and with the knowledge the students already have. Now that might be the knowledge that there is 128oz in a gallon or the knowledge of how to find out how many ounces are in a gallon.

The curriculum focuses on reaching the correct answer, not with one strict rule of getting the answer, but embracing the fact that there might be a number of different ways to get to the correct answer. It lets the students use everything they’ve already been taught to figure out the answers.

Here is a 7th-grade example:

Task

The price of a gallon of apple cider is $7.00. The price of eight 4.23-ounce juice boxes is $2.39.

    1. Suppose the juice was instead packaged like the cider. Approximately what is the cost per gallon of the juice?
    2. Suppose the cider was instead packaged like the juice. Approximately what is the cost per eight 4.23-ounce boxes of cider?
    3. Peter wants to have at least a gallon of either only cider or only juice. Which product is the better deal?
    4. State the unit rate(s) you used to compare the cost of cider versus juice in your answer to Question c.
    5. List two or more additional unit rates that could be used to make this comparison.

The following is the commentary given to teachers from Illustrative Mathematics:

This task asks students to compute multiple unit rates, aligning with standard 7.RP.A.1. The problem also has a real-world context, which requires students to compare two rates in different units in order to reach a conclusion on buying two different products.

There are a couple issues that may need to be addressed as students work through this problem. The first is that not all needed information is given for this task, namely, the conversion rate between gallons and ounces. Instructors can either let students look this up themselves or have it available for them, but ideally, students should come to the conclusion themselves that they need to know this conversion rate in order to continue. The second issue is that by “ounces” we mean “fluid ounces”. If students struggle with this distinction, it could be a good opportunity to discuss mass versus volume measurements, and how to tell by context which one is appropriate to use. There are 128 fluid ounces in 1 gallon.

Question e could be extended by asking students to compute some or all of the additional unit rates they listed, and to explain how these further support their answer to Question c.

This task could be implemented on its own as a handout for students, or, ideally, via the blog post which inspired it, which can be found at http://christopherdanielson.wordpress.com/2011/11/29/cider-price-rules/. The post could be displayed/distributed first to the whole class in order to generate a conversation prior to administering the task. This allows for students to connect with the real-world scenario they’re being put in, as well as to formulate their own guesses as to which product would be a better monetary buy and why.

Click here for the solutions to the task example.

As you can see from the example, students are given a real-world problem and are asked a series of questions to solve using the tools they should already have or use the tools they have to learn the parts they need to solve the questions.

The Illustrative Mathematics curriculum lets students use the math skill they’ve learned and will learn on a more consistent basis, which would allow for a deeper understanding of how to solve math problems and move away from a memorize this formula approach. Which is great in the long run.

In the short term, kids who have a hard time with word problems, in general, are going to have a period of adjustment we can be sure.

A bit of Illustrative Mathematics history

In 2011, Bill McCallum, former University of Arizona Distinguished Professor of Mathematics and lead author of the national standards known as the Common Core started working on Illustrative Mathematics.

“People wanted illustrations of the standards,” “They wanted sample tasks to help students understand what they’d need to know to meet the standard.” – Bill McCallum

It was an initiative of the UA Institute for Mathematics & Education, which was funded partly by the Bill and Melinda Gates Foundation, which also brought Common Core to many schools nationwide.

In 2014, McCallum started a new company called Illustrative Mathematics, which now acts as a clearing house for IM Certified Curriculum Partners such as McGraw Hill and Imagine Learning, currently used by the Bensalem School District. Think Imagine Math, that’s them.

Go to Math Night

If you’re the parent of a student going to Bensalem school, the event is open to Snyder, Shafer and 6th grade families. Take advantage of Math Night and find out what the heck Illustrative Mathematics is for yourself.

Experts from the University of Delaware will be on hand to answer all of your questions and any concerns you may have.

October 19th from 6 pm to 8 pm
Snyder Middle School
3330 Hulmeville Rd,
Bensalem, PA 19020

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