Students arrive at middle level or high school with different experiences and perspectives on what “doing math” means. Their families do, too. Every school year, families share common questions, such as:

- What are students actually doing in math classes today?
- Is it different from when I was in school?
- What do I need to know to set up my child for success in math this school year?
- How can I support my child throughout the year?

Hosting a Family Math Night at school can help answer these questions and bring a school community together. An effective and engaging way to structure a Family Math Night is to have it mirror a problem-based lesson in the classroom. This way, the focus is on math and learning rather than a monologue on procedures and policies.

## Establishing Learning Goals

As with any lesson, start with learning goals. For example, an overarching goal for a Family Math Night would be to begin a supportive, yearlong relationship of math learning. The goals for the event would be for participants to understand:

- How a problem-based lesson looks and feels
- How to develop the connection between what students are learning in class and any family support materials provided by the school
- How to access student and family materials

## Structuring a Family Math Night

Using the structure of a problem-based lesson, a Family Math Night at school will include an invitation to the mathematics, an in-depth study of concepts and procedures, and consolidation and application of what was learned.

### Step 1: Frame the experience. (10 minutes)

A good way to launch this event is to ask: “What does it mean to you to ‘do math’?” Ask participants to write down two or three words or phrases based on their own experiences. Then, invite participants to share. Record and display participants’ words or phrases for all to see—accurately and without judgment—just as teachers do in the classroom with their students.

### Step 2: Conduct a warmup. (10 minutes)

Choose an activity with a warmup from a curriculum lesson that invites everyone into the mathematics. Contextualize the lesson; explain how it fits into the unit’s narrative arc. For example, using the sample below, tell families, “This warmup helps anchor student thinking with equations and variables as they work with a more abstract task later in the lesson.” Give each participant a handout and facilitate the activity as directed by the curriculum.

**Sample lesson: Planning a Pizza Party**

Let’s write expressions to estimate the cost of a pizza party.

Sample warmup: A Main Dish and Some Side Dishes

Here are some letters and what they represent. All costs are in dollars.

*m* represents the cost of a main dish.*n* represents the number of side dishes.*s*represents the cost of a side dish.*t* represents the total cost of a meal.

- Discuss with a partner: What does each equation mean in this situation?

a. *m = 7.50 *

b. *m = s + 4.50*

c. *ns = 6*

d. *m + ns = t*

2. Write a new equation that could be true in this situation.

This warmup elicits the idea that an equation can contain only letters, with each letter representing a value. It also reminds students that an equation is a statement that two expressions are equal and that different expressions could be used to represent a quantity.

In addition to demonstrating the lesson the way students experience it in the classroom, the warmup gives family members time to train their own mathematical thinking. In this warmup, some participants may write out a new equation using words; others will use only the letters.

### Step 3: Conduct the lesson activity. (20 minutes)

The warmup segues into a lesson activity. The lesson activity is an anchoring experience meant to set the stage for what it looks and sounds like for the students to learn math this year. Choose an activity that is hands-on, involves some intuition outside of simply knowing or not knowing the math, and can be supported by mathematical tools. Keep in mind that this may be the first time families are engaging with a mathematical task from a problem-based curriculum, so they should feel supported as they work, be encouraged to collaborate, and experience moments of success.

**Sample activity: How Much Will It Cost?**

- Imagine your class is having a pizza party. Work with your group to plan what to order and estimate what the party would cost.
- What are some values you used that might change? Use letters to represent these variables.
- Write some expressions, equations, and inequalities to represent your thinking.

The sample activity prompts students to create expressions to represent the quantities and relationships in a situation, and it engages them in mathematical modeling. To facilitate the activity, arrange families into several small groups or tell them to work with three to four people near them. If necessary, explain terms such as “expression,” “equation,” and “inequality” using examples such as 3*c*, 2*n* +1 = 8, and *p* < 20.

After the groups work together, ask for feedback. For each idea, ask if the group had an equation or inequality that could represent the idea. If needed, help groups write equations or inequalities to represent constraints (like *n* < 30 for n representing the number of students in the class) and costs (like

### Step 4: Provide family support materials. (10 minutes)

Give each participant a copy of the student lesson summary and any family materials for that unit. To extend the experience of the lesson activity, invite families to read through the lesson summary, which should highlight key ideas, vocabulary, and examples. Encourage families to make connections and underline ideas they touched on in the warmup and lesson activity.

This is also a good opportunity to demonstrate how to access available family and student materials, as well as strategies for using them, such as using the materials to understand the content before jumping into homework, or supporting students who require extra practice. Explain the goals of the family materials, and ask families to read through them and use them with their child in the next few days.

### Step 5: Revisit the framing question. (10 minutes)

At this point, families have experienced three activities as a group: a warmup, a lesson activity, and reviewing the unit’s family support materials. To close, revisit the framing question: “What does it mean to ‘do math’?” Consider asking participants the following questions, and highlight key differences from words and phrases given earlier.

- What did it feel like to do math tonight?
- What felt different from what you remember about doing math when you were in school?
- How might this approach improve learning and understanding in math?
- Based on this experience tonight, how might students describe doing math this year?
- How can the resources we explored help you support your child this year?

## Mentioning Other Considerations

It is important to communicate expectations to families. If there are other items on the agenda for Family Math Night—such as a brief discussion of policies, expectations, or rules—the time spent on each section may be trimmed. Alternatively, if more than one hour is allotted, consider giving participants more time to explore the curriculum resources and brainstorm ways these resources could help them support their child at home.

## Sharing Mathematical Experiences

Over the course of the time together, there will be shared mathematical experiences that unite participants. These experiences might also shift some perspectives on what it means to “do math” and what it takes for students to be successful in a problem-based classroom. In one hour, a Family Math Night can begin fostering the attitudes and beliefs that are important in shaping a positive mathematical community.

**Ashli Black*** is a curriculum writer for Illustrative Mathematics, a nonprofit organization committed to creating a world where learners know, use, and enjoy mathematics. She is a National Board Certified Teacher in adolescent and young adulthood mathematics and taught high school math for six years.*