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.

I taught 6th grade math today while Kristi and her team attended ASCD. She asked me to work with our students on showing their work. Here’s the plan:

**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.

**Activities:**

- How long is Can’t Buy Me Love – Estimation180
- How long is We Will Rock You – Estimation180
- How long is I Feel Good – Estimation180
- Fruit Salad – IllustrativeMath

**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:**

- Fruit Salad – Illustrative Math

**Sample student work:**

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