How might we learn to show our work so that a reader understanding without having to ask questions? As we work with our young learners, we want them to grow as mathematicians and as communicators.

We ask students to show their work so that a reader understands without having to ask them questions. What details should we add so that our thinking is visible to others?

To show (and to assess) comprehension, we are looking for mathematical flexibility.

**Learning goals:**

- I can use ratio and rate reasoning to solve real-world and mathematical problems.
- I can show my work so that a reader can understanding without having to ask questions.

**Activity:**

- Jim and Jesse’s Money – Illustrative Math

**Learning progressions:**

Level 4:

I can demonstrate mathematical flexibility with ratio and rate reasoning to show what I know more than one way using tables, equations, double number lines, etc..

**Level 3:**

**I can use ratio and rate reasoning to solve real-world and mathematical problems.**

Level 2:

I can make tables of equivalent ratios relating quantities with whole-number measurements, and I can use tables to compare ratios.

Level 1:

I can use guess and check to solve real-world and mathematical problems.

**Anticipated solutions:**

- Jim and Jesse’s Money – Illustrative Math

**Using Appropriate Tools Strategically**:

I wonder if any of our learners would think to use a spreadsheet. How might technology help with algebraic reasoning? What is we teach students to create tables based on formulas?

How might we experiment with enough tools to display confidence when explaining my reasoning, choices, and solutions?

Choice of an appropriate tool is learner based. How will we know how different tools help unless we experiment too?