Outside the classroom, we thought about how our students differed - whether it was developmental readiness or how structured they liked their math to be. We prepared open and parallel questions by running through in our minds how those students might respond. In that way we verified whether our open or parallel questions make sense but you also anticipated some problems students might have so that we were prepared to scaffold. A scaffold is a temporary framework that is put up for support and access to meaning and taken away as needed when the child secures control of success with a task. The scaffolds provided by the teacher do not change the nature or difficulty level of the task; instead, the scaffolds - in the form of key questions - allowed the student to successfully complete the task. Scaffolding questions were not used as much to break questions up into bits for students, but to prompt their thinking in a relevant direction when they appeared stuck. We also thought hard about the math when creating the common questions to make sure they worked for the specific tasks provided.

**Open Questions:** An open question is a single question that can be used so that all of the learners in the classroom can participate and engage in meaningful mathematics.

For example, consider this question: An expression has a value of 12 when the variable ♥ in the expression is equal to 6.

What could the expression be?

This open question allows for many different responses, ranging from a very simple answer to a much more complicated one.

Eg. ♥ + 6 2 × ♥ 18 - ♥ 72 ÷ ♥ ♥2 + 2♥

Because we were asking students to come up with an expression for given input/output combination, it was much easier to differentiate the instruction. Students were usually asked to evaluate an expression for a given value of the variable. Sometimes the expression was difficult for a child or the calculation with a particular number might be difficult; in this situation students can control that sort of difficulty and more likely meet success.

For example, in relation to the open question above, the following scaffolding questions could be asked:

How do you know that the expression has a heart in it?

Could the expression have an addition sign?

Could the expression have a subtraction sign?

Could there be more than one heart in the expression? How many could there be?

Could the expression involve more than one operation?

Why is the heart the variable in the expression?

**Parallel Tasks:** Open questions not only allow for a range of difficulties in the solutions, but also can reinforce a wide range of mathematical concepts and skills. Open questions also provide choice, which is implicit in differentiating instruction. Students will answer the question in a way that is suitable for their cognitive level.

Parallel tasks are questions that focus on the same big ideas but have different levels of difficulty, taking into consideration the student readiness.

Consider the following question and choices:

Write each the phrase as an algebraic equation:

Option 1: Triple a number

Option 2: Add 1 to a number then double it

Both questions are asking students to work on the relationship between verbal expressions and algebraic ones. The first option had the student work with a phrase where only one operation is used. The second option had the student working with phrases that involve more than one operation. The big idea that is addressed in both options is that algebraic reasoning is a process of describing and analyzing generalized mathematical relationships and change using words and symbols.

The teacher planned common questions that focus on using the expression to represent the words.

Common questions:

What operation sign(s) appear in our expression? Why those?

Are there other ways to write your expression algebraically?

Did it matter which letter or symbol you used for your variable? Why or why not?

Could the words be slightly different but your expression the same? Explain.

In this video, the vice-principal is discussing the work of her teachers with Marian Small. Open questions and parallel tasks are the focus of the lessons and tasking questions that are inclusive. Open questions are ones that leave room for students to come at a broad idea in a manner of and often to an extent of their choosing. It is the student who, in essence, decides on the level of differentiation. With parallel tasks, the teacher anticipated how to change a problem or task to make it more accessible to a different group of students and so it was the teacher who controls the level of differentiation. In both cases, however, there was an underlying big idea which became the focus of discussion for all students.