Gearing Up for NC Exams

Recently, I have been collaborating with teachers on creating "practice" exams. We've developed a NC Math 1 Practice EOC and a NC Final Exam for Math 2.

I'm sharing here in case they can be beneficial for others.

• Math 1 Practice EOC Non-Calc  student booklet, answer key, solutions
• Math 1 Practice EOC CalcActive student booklet, answer key, solutions
• Math 2 Practice NCFE student booklet, answer key, solutions

I prefer to start with a blueprint design when creating assessments so I'm also sharing these with you. They should provide some additional information about the practice exams.

Math 1 Design,

Math 2 Design

Finally, I tweeted these out last semester and thought I should include them here as well. I compiled resources for review in NC Math 2 and NC Math 3. I organized them in a Google Sheet so I can continually add to and update.

**NC Math 2 Review Resources: http://bit.ly/Math2Rvw

**NC Math 3 Review Resources: http://bit.ly/Math3Rvw

As always, I appreciate any feedback as it is how we learn and grow. Best of luck to you and your students!!

Floating Down the River

In an effort to support teachers across the state with the implementation of the revised NC Math 1, 2, and 3 standards, the K-12 Mathematics team are hosting weekly webinars. Each Thursday focuses on a different course: Math 1, Math 2, Math 3, and Math Leaders. Find out more here.

The sessions present a math task (if you register early you will get it in advance) and frames the discussion on standards, implementation, anticipating student misconceptions, and connections.

This past month I was able to participate in the Math 1 and Math 2 sessions. The Math 1 session was on Functions and we were given the Floating Down the River task. (Which I tweaked a little. You can find the original version here.) I really like this problem especially to discuss the key features of the functions and interpreting them in context.

This is one of my SOAP BOX concerns: the difference between F-IF.4 and F-IF.7. When we discuss functions it quickly becomes about the "families of functions." You know the ones I am talking about - linear, quadratic, exponential, etc.). With these functions we are able to use the symbolic representation and determine key features. For example, rewrite a quadratic into vertex form and identify the vertex. This is F-IF.7.

So what is F.IF.4? It doesn't seem like it should be the same thing. IMHO - it is not. While F-IF.7 focuses on those classical function families, F-IF.4 is broader. It includes all functions. This includes functions I refer to as functions that tell a story. These functions may be represented symbolically, often by a piecewise function, which is well beyond the focus of Math 1. However, it is not unreasonable for students to reason with and interpret the key features using a table or a graph.

That's why I like the Floating Down the River task. Students are given multiple tables of values and a simple question is posed. I would expect students to do what we did during the session and graph the values. (Further commentary could be given on whether depth is positive or negative but I'll leave that up to you to decide.) Now, there are opportunities for students to discuss intervals of increase/decrease, maximum/minimums, average rate of change, and intercepts. They also have to compare and connect the events. Such as, when the water is shallow the speed increases. Can students also recognize that the distance function becomes steeper? Will they recognize why that would be occur?

There is great potential in the task which is why I am encouraging my teachers and sharing with you. Try it and see what students do with it. I guarantee learning will take place. Also, consider joining me and others at the next Math 1 webinar.

The 1st Day of School

What should students do on the first day of math class? It seems that the standard introduction includes a syllabus, grading policy, rules, and procedures. What seems to be debatable is whether or not students should do math on the first day. Huh?

When I think about the first day, I want to clearly communicate expectations. One of the expectations is that everyone will engage in the teaching and learning of math on a daily basis. This means every day - including the first day.

The first day would include making sure the students are in the right class, briefly introducing myself, go over three rules (Be Ready, Be Responsible, Be Respectful), and then do a math task.

What kind of tasks are good for the first day? I look for a task that:

• is engaging / interesting
• has students collaborating
• has multiple entry points for students
• has multiple solution methods
• includes math ideas that launches the first unit of study (if possible)

One of my favorite tasks for Math 1 is Crossing the River. The premise is that there are 8 adults and 2 children that need to cross a river. The boat can hold either one adult OR one child OR two children.

The Launch: (I like to tell stories to engage students in the situation. So I tell them...)

Calderwood Lake - The Men's Camping Trip

My husband and son go on a Men's Camping trip every fall. On one of these trips they were going to hike around the lake. Eight of the men, my son, and another young boy took off early in the morning. When they were about halfway around the lake, the sky began to get cloudy and it appeared that a storm was arriving. One of the men noticed a boat and suggested they take the boat across the lake to quickly get back to the campsite. Testing the capacity of the boat, they determined that only one adult OR one of the boys OR both of the boys could be in the boat at one time. Now what?

Students are provided the opportunity to ask questions. These include:

• Are the boys capable of rowing the boat on their own? Is it safe?
• Should they be taking a boat that doesn't belong to them?
• Is there rope so they can pull it back across?
• How much time would it take for them to walk back or continue on?
• How much time does it take to get across the lake?
• How many trips would it take to get everyone across the lake?

The types of questions students ask indicate if students are thinking quantitatively. The first few questions are about the situation but not ones we can explore. The last few questions are ones that involve some quantitative reasoning. After the questions are posed, we discuss which ones can be explored with the information we have at hand. The last question is the one we focus on.

The Exploration:

I inform students that there are materials available for their use located in the resource center. These include paper, colored paper, graph paper, rulers, chips of different colors, scissors, etc. (Doing this on the first day introduces students to the resource center and sets the procedure that they can access these tools whenever they need something.)

Students work in groups to determine an answer to the question. (I prefer groups of 3 and no more than 4.) Some draw pictures while others get the color chips and begin manipulating them back and forth across an imaginary or sometimes drawn lake. Eventually, they determine the number of trips. I ask extension questions to groups. What if there were 15 adults? 30 adults? What if there were 5 kids? 

The Share Out:

For this activity I tend to focus on the different ways groups approached the problem. I select and sequence how groups share with the intent of creating opportunities for students to compare their methods; understanding the differences and the similarities.

Reflection:

Now that the students have a shared common experience I use it to discuss expectations such as making sense of problems, collaboration and student discourse.

For the next two weeks students will learn the different procedures for the classroom when they need to know them. For example, where do they put papers that need to be turned in? We will go over this the first time they have something to turn in. Another example, what is the procedure for leaving the classroom? I go over this the first time a student asks. I have determined that students often don't really learn the procedures for the classroom until it becomes something they recognize they need to know.

The first day focuses on the expectation that math class will be about developing and exploring ideas using math.